How can I subdivide a lattice?
A lattice is not an actual mesh, and is in reality more akin to an array of hook empties. So, just like an empty, you can't edit in edit mode. However, there is a way to subdivide it. Go to Properties > Data and you can change the resolution for the height, width, and depth. Note that these are relative, so rotating will quite possibly make the top on the bottom, or the right on the left.